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We design arbitrarily high-order accurate entropy stable schemes for systems of conservation laws. The schemes, termed TeCNO schemes, are based on two main ingredients: (i) high-order accurate entropy conservative fluxes and (ii) suitable numerical diffusion operators involving ENO reconstructed cell-interface values of scaled entropy variables. Numerical… (More)

We present a streamline diffusion shock capturing spacetime discontinuous Galerkin (DG) method to approximate nonlinear systems of conservation laws in several space dimensions. The degrees of freedom are in terms of the entropy variables and the numerical flux functions are the entropy stable finite volume fluxes. We show entropy stability of the… (More)

- Bernardo Cockburn, Johnny Guzman, Haiying Wang, Long Chen, Michael Holst, Jinchao Xu +18 others
- 2010

1 Superconvergent discontinuous Galerkin methods for second-order elliptic problems / A multiscale finite element method for partial differential equations posed in domains with rough boundaries / Alexandre L. Madureira 35 Convergence and optimality of adaptive mixed finite element methods / 79 Overlapping additive Schwarz preconditioners for elliptic PDEs… (More)

We consider a scalar conservation law with a discontinuous flux function. The fluxes are non-convex, have multiple points of extrema and can have arbitrary intersections. We propose an entropy formulation based on interface connections and associated jump conditions at the interface. We show that the entropy solutions with respect to each choice of… (More)

We prove that the ENO reconstruction and ENO interpolation procedures are stable in the sense that the jump of the reconstructed ENO point values at each cell interface has the same sign as the jump of the underlying cell averages across that interface. Moreover, we prove that the size of these jumps after reconstruction relative to the jump of the… (More)

The Multi-Level Monte Carlo finite volumes (MLMC-FVM) algorithm was shown to be a robust and fast solver for uncertainty quan-tification in the solutions of multi-dimensional systems of stochastic conservation laws. A novel load balancing procedure is used to ensure scal-ability of the MLMC algorithm on massively parallel hardware. We describe this… (More)

β-glucosidase from Withania somnifera (Solanaceae) leaf has been purified to homogeneity and characterized for its physico-kinetic properties. The enzyme purification was achieved through a sequence of gel filtration and ion-exchange column chromatography, and PAGE revealed the homogeneity purification status of the enzyme. The properties of the enzyme… (More)